BC Fall Review.

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Presentation transcript:

BC Fall Review

Give the first 4 non-zero terms of the MacClaurin Series for the function: Hint: You don’t need to generate each term. Check your notes/book. Use P(x) to find the first 4 non-zero terms for arctan(x)

Since we already know that arctan(0) = 0, we know that C = 0 Use this result to approximate Find the maximum error involved in this approximation.

Use this result to approximate Find the maximum error involved in this approximation. Because this is an alternating series, we use the next term to find the error.

Use this result to approximate Find the maximum error involved in this approximation. Because this is an alternating series, we use the next term to find the error.

Generate a 2nd degree polynomial to approximate ln(0. 9) and ln(1. 1) Generate a 2nd degree polynomial to approximate ln(0.9) and ln(1.1). Find the error bound involved in each approximation.

Generate a 2nd degree polynomial to approximate ln(0. 9) and ln(1. 1) Generate a 2nd degree polynomial to approximate ln(0.9) and ln(1.1). Find the error bound involved in each approximation. Because this is an alternating series, we can just use the next term… Because this is no longer an alternating series, we need the Lagrange error bound for the 3rd term…

Generate a 2nd degree polynomial to approximate ln(0. 9) and ln(1. 1) Generate a 2nd degree polynomial to approximate ln(0.9) and ln(1.1). Find the error bound involved in each approximation. Because this is no longer an alternating series, we need the Lagrange error bound for the 3rd term… And the number between 0.9 and 1 that maximizes this value is 0.9

Find the radius and interval of convergence:

Use the integral test to determine if the given series converges: …and therefore it converges

Use the integral test to show that the given series converges 1) Find the sum to which it converges. 2) 1)

Use the integral test to show that the given series converges 1) Find the sum to which it converges. 2) 1) …or more importantly, since we have a finite limit, the series converges.

Use the integral test to show that the given series converges 1) Find the sum to which it converges. 2) 2)

Evaluate the integral:

Evaluate the integral: x  2

Evaluate the integral: x  2

Indeterminate L’Hopital’s Rule